Honestly, I'd skip Nazare completely. Lots of tourists, a beach, tacky shops and some seafood restaurants. Put your days somewhere, anywhere, else. Evora, on the other hand, is really worth it. The neolithic sites are interesting, but take a tour for the best experience. We had a guide take us to a cork farm, which was interesting. Actually, she was a co-owner, so she had a lot of knowledge and enthusiasm.
We had a car, so I can't comment on the train/bus connections. We stayed at Albergaria do Calvario, our second choice, and we weren't disappointed. It was lovely. The property was sold by the couple mentioned in the last RS Portugal guide, but the new owners were friendly and helpful. The room was spotless and the breakfast was great. It has an elevator and parking, too. It wasn't as expensive as the pousada in town.
We'd recommend Taberna Tipica Quarta-feira and Restaurante O Fialho, but it's best to either eat very early or make a reservation at both. Out in the countryside, in Santiago do Escoural is Rabinos, which was outrageously great and so inexpensive I couldn't believe the prices. It's simple, hearty food. of the Alentejo. It's about 30 minutes outside of Evora, and well worth the drive.